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SAT Math : Decimals

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Example Questions

Example Question #373 : Arithmetic

Find the square root of the following decimal:

$\small \sqrt{0.00036}$

Possible Answers:

$\small 0.006$

$\small 0.06$

$\small 0.013$

$\small 0.019$

Correct answer:

$\small 0.019$

Explanation:

This problem becomes much simpler if we rewrite the decimal in scientific notation

$\small 0.00036 = 3.6\times 10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can take its square root by dividing it by two. The square root of 4 is 2, and because 3.6 is a little smaller than 4, its square root is a little smaller than 2, around 1.9

$\small \sqrt{0.025} = \sqrt{3.6}\times \sqrt{10^{-4}} \approx 1.9\times 10^{-2} = 0.019$

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Example Question #374 : Arithmetic

Find the square root of the following decimal:

$\small \sqrt{0.00064}$

Possible Answers:

$\small 0.0253$

$\small 0.008$

$\small 0.08$

$\small 0.8$

Correct answer:

$\small 0.0253$

Explanation:

To find the square root of this decimal we convert it into scientific notation.

$\small \small 0.00064 = 6.4 \times10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, and the square root of 4 is two, so the square root of 6.4 is between 3 and 2, around 2.53

$\small \small \sqrt{0.00064} = \sqrt{6.4}\times\sqrt{10^{-4}} \approx 2.53 \times10^{-2} = 0.0253$

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Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

$\small \sqrt{0.0169}$

Possible Answers:

$\small 0.0411$

$\small 0.0285$

$\small 0.13$

$\small \small 0.0318$

Correct answer:

$\small 0.13$

Explanation:

To find the square root of this decimal we convert it into scientific notation.

$\small \small 0.0169 = 169\times10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root. $\small 169$ is a perfect square, whose square root is $\small 13$ .

$\small \small \sqrt{0.0169} = \sqrt{169}\times \sqrt{10^{-4}} =13\times10^{-2} = 0.13$

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Example Question #4 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

$\small \sqrt{0.00001}$

Possible Answers:

$\small 0.0001$

$\small 0.001$

$\small 0.01$

$\small 0.00316$

Correct answer:

$\small 0.00316$

Explanation:

To find the square root of this decimal we convert it into scientific notation.

$\small \small \small 0.00001 = 10 \times10^{-6}$

Because $\small \small 10^{-6}$ has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, so the square root of 10 should be a little larger than 3, around 3.16

$\small \small \sqrt{0.00001} = \sqrt{10}\times \sqrt{10^{-6}} = 3.16\times10^{-3} = 0.00316$

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Example Question #375 : Arithmetic

Find the square root of the following decimal:

$\small \sqrt{0.004}$

Possible Answers:

$\small 0.016$

$\small 0.0632$

$\small 0.002$

$\small 0.02$

Correct answer:

$\small 0.0632$

Explanation:

To find the square root of this decimal we convert it into scientific notation.

$\small \small 0.004 = 40 \times10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 36 is 6, so the square root of 40 should be a little more than 6, around 6.32.

$\small \small \small \sqrt{0.004} = \sqrt{40}\times\sqrt{10^{-4}} \approx 6.32 \times10^{-2} = 0.0632$

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Example Question #4 : How To Find The Square Root Of A Decimal

Solve for :

$\frac{x}{\sqrt{0.04}}=\sqrt{0.16}$

Possible Answers:

0.64

0.2

0.08

0.4

Correct answer:

0.08

Explanation:

Just like any other equation, isolate your variable. Start by multiplying both sides by $\sqrt{0.04}$ :

$x=\sqrt{0.16}*\sqrt{0.04}$

Now, this is the same as:

$x=\sqrt{0.0064}$

You know that $\sqrt{64}$ is . You can intelligently rewrite this problem as:

$x=\sqrt{0.0064}=\sqrt{\frac{1}{10\textup{,}000}*64}$ , which is the same as:

$\sqrt{\frac{1}{10\textup{,}000}*64}=\sqrt{\frac{1}{10\textup{,}000}}*\sqrt{64}=\frac{1}{100}*8=0.08$

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Example Question #32 : Decimals

Find the square root of the following decimal:

$\small \sqrt{0.00000025}$

Possible Answers:

$\small 0.005$

$\small 0.0005$

$\small 0.00025$

0.00158

Correct answer:

$\small 0.0005$

Explanation:

To find the square root of this decimal we convert it into scientific notation.

$\small \small 0.00000025 = 25 \times 10^{-8}$

Because $\small \small 10^{-8}$ has an even exponent, we can divide the exponenet by 2 to get its square root. $\small 25$ is a perfect square, whose square root is $\small 5$ .

$\small \small \sqrt{0.00000025} = \sqrt{25}\times \sqrt{10^{-8}} = 5\times10^{-4} = 0.0005$

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Example Question #381 : Arithmetic

Evaluate: $\sqrt{1.44}$

Possible Answers:

$\pm1.2$

$\pm0.12$

0.0012

$\pm0.012$

1.2

Correct answer:

$\pm1.2$

Explanation:

The square root of a number returns a positive and negative number that multiplies by itself to obtain the number inside the square root.

$\sqrt{1.44}= \pm1.2$

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Example Question #12 : How To Find The Square Root Of A Decimal

Without using a calculator, solve for x:

x^2 = 0.16

Possible Answers:

$\pm0.4$

$\pm\frac{2}{\sqrt{10}}$

$\pm0.9$

$\pm0.8$

$\pm0.5$

Correct answer:

$\pm0.4$

Explanation:

Simplifying the given equation gives us

$x=\pm\sqrt{\frac{16}{100}}=\pm\frac{\sqrt{16}}{\sqrt{100}}$

$=\pm\frac{4}{10}=\pm0.4$

Therefore, the correct answer is $\pm0.4$ .

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Example Question #383 : Arithmetic

If x^2=0.000004 and x>0 , what is the value of ?

Possible Answers:

0.002

0.02

0.2

0.0002

Correct answer:

0.002

Explanation:

We are given the equation x^2=0.000004 . To determine the value of , take the square root of both sides.

$x=\sqrt{0.000004}$ .

To calculate this value, take note of the following pattern:

$\sqrt{4}=\pm2$

$\sqrt{0.04}=\pm0.2$

$\sqrt{0.0004}=\pm0.02$

Each succeeding radicand is $\frac{1}{100}$ of the previous radicand, and the value of each succeeding square root is $\frac{1}{10}$ of the previous value. Continuing the pattern:

$\sqrt{0.000004}=\pm0.002$ . However, we are also given the condition that x>0 ; hence, we eliminate the extraneous solution x=-0.002 and conclude that the only valid solution of x^2=0.000004 is x=0.002 .

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SAT Math : Decimals

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #373 : Arithmetic

Example Question #374 : Arithmetic

Example Question #1 : How To Find The Square Root Of A Decimal

Example Question #4 : How To Find The Square Root Of A Decimal

Example Question #375 : Arithmetic

Example Question #4 : How To Find The Square Root Of A Decimal

Example Question #32 : Decimals

Example Question #381 : Arithmetic

Example Question #12 : How To Find The Square Root Of A Decimal

Example Question #383 : Arithmetic

All SAT Math Resources

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